Optimal investment under inflation protection and optimal portfolio With stochastic wage income

Abstract

This dissertation considers the optimal portfolio strategies for an investor that obtains stochastic income and gives out stochastic cash outflows under inflation protection. The Investor trades on a complete diffusion model, receives a stochastic wage income and pays a stochastic cash outflow to its holder. The stochastic income is invested into a market that is characterized by a cash account, an inflation linked bond and a stock. The inflation risks associated with the investment could be hedged by investing in inflation-linked bond. The solutions to the Investor problem of seeking the optimal portfolio are formulated and worked out as stochastic control problem. The cash account is deterministic, and the inflation-linked bond and the stock are geometric. The optimal portfolio strategies for this Investor are solved and the utility function considered is assumed to be a quassi-concave function of the value of wealth and power utility is utilized. The optimal portfolio of the Investor in the cash account, in the inflation linked bond, and in the stock market were established.